How to Solve Logarithmic Equations with Different Bases - The Change of Base Formula

[@damianmatma708]

00:00 It is even more simple when you use the formula: log.(a^m) (x) = (1/m) * log.a(x) Hence you get: log.8(x) - log.16(x) = 0 log.(2^3)(x) - log.(2^4)(x) = 0 (1/3) * log.2(x) - (1/4) * log.2(x) = 0 Now it is quite simple: [ (1/3) - (1/4) ] * log(x) = 0 [ (4/12) - (3/12) ] * log(x) = 0 (1/12) * log(x) = 0 || *12 log(x) = 0 log.10(x) = 0 x = 10^0 x = 1 "1" is the solution, because it is in the Domain which is D: x>0

[@unonovezero]

I came up with the same solution as yours, before watching the video and comments. It's quicker and without unuseful steps.

[@sanelephungula8780]

For those of you telling sir that he could have solved the problem in three steps keep your mouth shut, he's a professor he knows wat he's doing and his intentions was to clearly illustrate for students that might not readily know how to go about solving this problem problem, thank you.

[@PreMath]

Thank you so much! Please keep supporting my channel. Kind regards 😀

[@mekdalwityoseph1100]

All humans have mistake except Lord Jesus and his mother virgn Mary and being professer doesn't make him knowing every thing and not to do mistake expect tirinty lord

[@EE-Spectrum]

I strongly disagree with you. In an exam students need the shortest possible mathematical way to solve problems. They don't need complicated methods and he being a professor should know that.

[@global-linkacademicagency2156]

Just because he's a professor doesn't make everyone else an idiot.

[@ddouglas8161]

I love this. One thing I wanted to add to gues video is that being log8(x) and log16(x) have base 2 in common, we could rewrite it as log2^3(x) and log2^4(x) and identifying a log base value would be the denominator when the change of base is applied, we could then rewrite the equation as 1/3log2(x)-1/4log2(x) and then proceed from there.

[@pierrepicard762]

0pplp0pd0lo 0poppp0pp0

[@prathamdivyansh2376]

And further take value of log2(x) to be t solve t it only gives one value which is 1 and solve less lengthy

[@johnporcella2375]

Excellent tutorial covering, ahem, a lot of bases! No pun was intended!

[@harshmaurya3848]

A man who makes totally time wasting short videos has 10 million subscribers in his channel but this channel is really awesome and has only approx 2 lakh. Not fair yaarrr

[@josepmadrid5400]

These people were trying to outsmart the teacher.really? Why waste watching if you know already and know quick solution? ..this lecture is for those students or person who has difficulty and willing to understand it step by step. Just be humble guys, make ur own KZbin channel..

[@jaaaayt.20]

i liked and watched the video sir

[@PreMath]

Thanks. You are awesome.

[@henrydavis8910]

It was obvious from the beginning that log x = 0, meaning x = 1, because the only way that raising x to two different powers gives an equality is if x = 1. This fellow used a sledgehammer to kill a fly. Far too complicated, tedious, and unnecessary.

[@geoellinas]

Yes. The charm of mathematics is in finding the shortest path!

[@john-phimcmelley6422]

I agree. And whatever the base is, log 0 is undefined, so the solution x=0 must be rejected before any calculus. (Always check the domain before starting !)

[@humphreyfrog2045]

@@geoellinas I think the charm of mathematics is paths

[@geoellinas]

@@john-phimcmelley6422 For mathematicians yes. But for the students I believe what I said.

[@gregnixon1296]

It amazes me how many answers are -1, 0, or 1.

[@GreatBearLullaby]

I love this. Two logs have different base and are equal. How's that? So that x = 1. Just because no other points where different-base logs can meet. Telling this basic story during nine minutes - great.

[@matthewtaylor8102]

Change of base, seems to suggest Gauge equation: unit conversion transform method. Conductance, energy, conversion and energy transform ascertained. Thanks and have a nice day, thank you Sam.

[@Demi305]

I have a Little doubt, sir At 6:30, you got X⁴ = X³, so as the bases are equal, we get 4 = 3 but 4 ≠ 3, I am a bit confused, could you please reply However, Thank you very much for this amazing video, I have been actively watching a lot of your videos and they have really amazed me! Keep it up! hope to see more!

[@unnati_hulke]

If you try putting up the value of x as 1 or 0, the equation X³ = X⁴ will become valid, as we know, 1 to the power of n = 1; thus X³ = 1; X⁴ = 1; hence X³=X⁴ And. For x=0, 0^n = 0. Hence X³ =X⁴ =0 This won't work out on other values, except for 0 and 1... Hope you got my point....

[@john-phimcmelley6422]

The log function is not defined on the interval ]-∞, 0]. You MUST state that BEFORE begining any calculus, hence excluding 0 as a solution. Thus checking the answer x=0 as you do is unnecessary (not to say wrong).

[@kabelingo5418]

There is a short solution. You solve the right side y= log.16 (x) by taken it to the base (2*8) . y is only a placeholder for the watched term. So (2*8)^y=x eq(1). This can be simplified to 2^y*8^y=x (eq2). Now the left side is taken to base 8. So y=log.8 (x) becomes 8^y=x eq(3) , which can be written as 2^y*2^y*2^y=x. Now taken the 3. root from that: 2^y=3.root(x) (eq4) eq(3) and eq(4) we set in eq(2) and we get 3.root(x)*x=x. We can see the possible solution are x=0 and x=1. But x=0 is no solution, because the original equation get infinity. It remains x=1

[@abdurahmanmuse2941]

Really, exciting Vedio 🔥😇

[@nadeekaekanayeka.9347]

The lesson is well understood sir,thanks a lot.

[@MS-cj8uw]

Sir the solution is maximum 3 steps only ....

[@homayounshirazi9550]

We used to get points taken off for "excessive math!"

[@charlynecharles8649]

hes trying his best, so dont be so rude

[@jennybenson9562]

can you explain to me how it is easier? I am in a math class at my college and I want to understand how it can be done in 3 steps

[@ziadahmed6955]

Form the very begining you can take logx as a common factor then you will see that log x times 1/log8 minus 1/log16 equal zero which means that logx equal to zero therefore x equal 1

[@tapatirudrapal5586]

@@jennybenson9562 o .i see.u r in college but also u r not able to use a simple logarithmic equation

[@natashachisenga9524]

I need some of your previous videos on logs

[@jemanishajones9707]

I watched and liked it

[@PreMath]

Thanks. You are awesome.

[@sriiniketansridhar1944]

Sir, usually when doing this problem you also have to add two with log of x

[@muhammadtareq6253]

Hi Sir, just wonder about this part x^4 = x^3, Couldn't you just divide both sides by x^3 so you could find just the true answer right away? Thanks anyway way.

[@albertmendoza1468]

x^4=x^3 is not possible

[@tigerbeast3406]

@@albertmendoza1468 It's possible if x is equal to 0 or 1

[@SrisailamNavuluri]

When x=0,you are dividing by 0.

[@war_reimon8343]

@@tigerbeast3406 0 is not possible because it is undetermined. So it leaves only possible the one.

[@tigerbeast3406]

@@war_reimon8343 You must factor it to find all the real solutions x^4 = x^3 x^4 - x^3 = 0 (x^3)(x - 1) = 0 (factoring x^3) The two solutions are: x^3 = 0 or x - 1 = 0 Therefore from the first equation x = 0 and from the second we get x = 1

[@renewd]

I used log.2 when using the change of base formula, this eliminated many of the steps. i only arrived at 1 solution, x = 1.

[@zolisaganyile1128]

So far so good 👍

[@jim2376]

This guy is an excellent teacher.

[@anandamondal6092]

At starting point can be eliminate logx from boths side, then how can get x value?

[@Kidaniekidanie]

Thanks a lot sir,

[@tryyourbest3162]

I am Bangladeshi 🥰🥰🥰 thanks a lot ❤️

[@charlotteserimbi4862]

May God almighty bless you

[@nasimultafim765]

Had a confusion about the base changing of a logarithm. It totally solved the problem. Appreciate it👏

[@hungryfareasternslav1823]

Sir, you don't need to do that long since log_n(1)=0

[@ramanivenkata3245]

Fantastic explanation 👍

[@PreMath]

So nice of you Ramani dear! You are awesome 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and stay blessed😃

[@tapatirudrapal5586]

u have made it an equation history.it could be solved more easierly

[@AmirgabYT2185]

x=1

[@JLvatron]

At 1:34, you have Log X on both sides. If we divide by this we will have 1/Log 8 = 1/Log 16. How can this be?

[@JLvatron]

@@XJWill1 Thanks!

[@giovannisala9242]

Lo scopo dell'esercizio proposto e la sua soluzione, è anche di mostrare molte belle proprietà dei logaritmi e le molte ed eleganti vie del calcolo.

[@kyikyilay6119]

Thank you so much .

[@thichhochoi766]

At 2:59 log (x)/a = log(x)/b is impossible unless log (x) = 0 or x=1.

[@sriramtejapalika3605]

Sir, can you do this problem

[@damianmatma708]

03:45 You should rather put this "(1/4)*log(x)" form the right side to the left side (with the sign "+" changed to "-"): (1/3)*log(x) = (1/4)*log(x) (1/3)*log(x) - (1/4)*log(x) = 0 [ (1/3) - (1/4) ] * log(x) = 0 [ (4/12) - (3/12) ] * log(x) = 0 (1/12) * log(x) = 0 || *12 log(x) = 0 log.10(x) = 0 x = 10^0 x = 1 "1" is the solution, because it is in the Domain which is D: x>0

[@dadsprincess158]

Sir please give solution for this If log a basex=log b base x thena=b if where a>0^b>0^ x>0 x is not equal to 1

[@PreMath]

Hello Eshwaraiah, here is the proof: Our LHS: log a basex=log b base x => use the change of base formula: (loga)/(logx) = (logb)/(logx) => both denominators get cancelled => loga = logb => use equality rule: a=b RHS. Hope it helps. If you want I can upload video for you as well. Take care and all the best😃

[@misterywhawee8182]

Can you say that cause X^3 = X^4 so it have to be 1 and 0 otherwise its not possible?

[@johngreen3543]

Instead of using base 10 it is easier if you use base 2 on the change of base

[@Awesome-1001]

What i did at the end where we have: X^⅓ = X^¼ is: Divide both sides by X^¼ X^⅓/X^¼=1 Move the X^¼ to the numerator and get: X^⅓*X^-¼=1 X^1/12=1 (X^1/12)^12=1^12 X=1

[@ruthmuhambe776]

Thanks for that

[@jonathanaryee3505]

I didn't do it that same way but still had an answer. I got to a part of 4INX - 3INX which is equal to zero. Then I subtracted 3 from 4, which which made it e of x is equal to zero. Then I had x to be one.

[@edwinalexander1170]

X should only be equal to 1 sir as log of zero to any base is under define

[@ItumelengS]

Yep, and it can only be one value as it's only x^1

[@aakashkarajgikar9384]

Dude! I did it the easier way out. First, what I did is, used the change of base formula ; then rewrote 16 as 2^4, and 8 as 2^3 ; then I used the power rule of logs "log(n^b) = b * log(n)" ; then I multiplied both of the fractions to get common denominators ; then I set just the numerator equal to zero after setting the whole fraction equal to 0 ; then I used the power rule of logs in reverse "b * log(n) = log(n^b)" ; then I used the quotient rule of logs ; then I used the quotient rule of exponents within the logs ; then I set log(x) to be equal to log(x) with base 10 ; then I converted to exponential form ; then noticed 10^0, which is equal to 1, and that is equal to x. What you are doing is the longer way out. you are checking for more possible solutions, but they are extraneous, so it would have been better if you did what I did no?

[@thinklogically3081]

I think x = {0,1,2,3,4,5,6,7} , what is your idea

[@harrymatabal8448]

Mr sanel he is a professor of what. I can also call you professor

[@IanWadhare]

Why do you go long distance

[@timtran7756]

thanks

[@PreMath]

You're welcome Tim! Thank you. You are awesome😀 Keep smiling😊 Enjoy every moment of your life 🌻

[@war_reimon8343]

Only 1 fulfills the equation.

[@samriddhbhattacharyya6350]

I think we can solve this problem in another way avoiding all the complicated calculations Logically how can the power of 8 and 16 be same for the same value unless the value is 1 and power is 0 hence x has to be equal to 1

[@tonyhoanghp]

Good

[@harrymatabal8448]

(log x)/(log 8) = (log x)/log16 Log 8 = log 16 8 = 16 Where did I make a mistake professor

[@charlotteserimbi4862]

I am understanding

[@luyandomweemba4103]

Amazing..

[@PreMath]

Thank you so much luyando mweemba for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Please stay connected. Take care dear 😃

[@gelbkehlchen]

Solution: (1) log8(x) - log16(x) = 0 According to logc(y) = loga(y)/loga(c) = same base (number/base), the following applies: log16(x) = log8(x)/log8(16) | applied in equation (1), results in: (1a) log8(x)-log8(x)/log8(16) = 0 |*log8(16)≠0 ⟹ (1b) log8(x)*log8(16)-log8(x) = 0 ⟹ (1c) log8(x)*[log8(16)-1] = 0 |/[log8(16)-1]≠0 ⟹ (1d) log8(x) = 0 ⟹ x = 8^0 = 1 Lösung: (1) log8(x)-log16(x) = 0 Nach logc(y) = loga(y)/loga(c) = gleiche Basis (Numerus/Basis) gilt: log16(x) = log8(x)/log8(16) | in Gleichung (1) angesetzt, ergibt: (1a) log8(x)-log8(x)/log8(16) = 0 |*log8(16)≠0 ⟹ (1b) log8(x)*log8(16)-log8(x) = 0 ⟹ (1c) log8(x)*[log8(16)-1] = 0 |/[log8(16)-1]≠0 ⟹ (1d) log8(x) = 0 ⟹ x = 8^0 = 1

[@蕭嘉誠-f2h]

Why the answer not x=1?

[@shanaya9876]

I almost solved this but got stuck at the end cause of splitting of x4-x3😅

[@adgf1x]

logx b2/3-logxb2/4=0=>logxb2=0=>x=2^0=1ans

[@senghour8043]

log(🐭) ×log(🐭) =[log(🐭)] ×2 or [log(🐭)]?😔😔

[@adgf1x]

Log of x base2=0=>2^0=x=>x=1

[@buttsez4419]

It was obvious Why complicate things

[@ruilongsheng2845]

log x/3log 2 =log x/4log 2, so log x=0, x=1😃

[@sriramtejapalika3605]

3^(x-1) =5

[@kelticlago]

C'est une farce?

[@9mmomo]

Ouais c’est farce, x=1

[@akashranjanmohapatra4302]

Where will be 12

[@daniel.gutierrez18333]

Can somebody solve 4^ = 2^x

[@neelamsrivastava8577]

X=2

[@pranavamali05]

I got answer as 12

[@faithelias2798]

God loves you and he wants to save everyone, but in order for him to do that, you need to repent and be baptized. Also share his gospel with everyone you come in to contact with and keep his commandments 🙏🏾😘

[@meshackokuomose2067]

X is 1

[@SaidAli-y4u]

Ok

[@hmza7227]

diwiiided buy

[@에스피-z2g]

logx/log8=logx/log16 logx=0 x=1

[@HHH-tt5sb]

حلك غير صحيح ﻻن المعادلة ﻻتتحقي اﻻ عندماx تساوي الصفر

[@giuseppemalaguti435]

solo a vederla mi sembra non abbia soluzioni

[@henriquevianna6875]

Elementary school math

[@giuseppemalaguti435]

forse 1

[@AthenaFidelia]

Pliz h

[@cuongtu6088]

it long

[@Darkdesires946]

Why is it so confusing😂

[@mulinakashala1st821]

mind twisted already

[@doichekabano]

Воды много, автор объём нагоняет...

[@oldsachem]

Too many steps.

[@JONATHANPHONES]

Wrong dull teacher

[@AnuragYadav-zk5pe]

haaa

[@patrickstewart6090]

log x 8 = 3/2 how to solve

[@역학적에너지-i9z]

x^(3/2)=8 x=8^(2/3) 8^(2/3)=(8^(1/3))^2=2^2=4 x = 4 and, 4^(3/2)=8 Q.E.D (actually, this problem's solution is logarithme's definition.)

[@mohamudmohamedyusuf2858]

@@역학적에너지-i9z xnxc

[@daniel.gutierrez18333]

Can somebody solve 4^x = 2^x

[@HoutarouOrekiOsu]

(2^2)^x = 2^x 2^2x = 2^x 2x = x 2x - x = x - x x = 0

[@adgf1x]

x=1